{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TOY DATA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#require(IRdisplay)\n",
    "\n",
    "#display_html(\n",
    "#'<script>  \n",
    "#code_show=true; \n",
    "#function code_toggle() {\n",
    "#  if (code_show){\n",
    "#    $(\\'div.input\\').hide();\n",
    "#  } else {\n",
    "#    $(\\'div.input\\').show();\n",
    "#  }\n",
    "#  code_show = !code_show\n",
    "#}  \n",
    "#$( document ).ready(code_toggle);\n",
    "#</script>\n",
    "#  <form action=\"javascript:code_toggle()\">\n",
    "#    <input type=\"submit\" value=\"Click here to toggle on/off the raw code.\">\n",
    "# </form>'\n",
    "#)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "    source(\"http://data.vanderbilt.edu/tgs/misc/r_functions.txt\")\n",
    "    require(Hmisc)\n",
    "    require(knitr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n",
    "set.seed(2340)\n",
    "N <- 1e5\n",
    "data <- data.frame(\n",
    "    id               = 1:N,\n",
    "    age              = sample(18:75,          N, replace = TRUE, prob = 1/(5 + abs(18:75 - 55))),\n",
    "    sex              = sample(c(\"M\",\"F\"),     N, replace = TRUE),\n",
    "    race             = sample(c(\"W\",\"B\",\"O\"), N, replace = TRUE, prob = c(3,2,1)),\n",
    "    diabetes         = sample(c(\"Y\",\"N\"),     N, replace = TRUE, prob = c(2,4)),\n",
    "    disease_severity = rchisq(N,2)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CATEGORICAL VARIABLES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Descriptive Statistics  (N=100000)\n",
      "\n",
      "+----------------+--------------+\n",
      "|                |              |\n",
      "|                |(N=100000)    |\n",
      "+----------------+--------------+\n",
      "|age             |   43/54/60   |\n",
      "+----------------+--------------+\n",
      "|sex             |              |\n",
      "+----------------+--------------+\n",
      "|    F           |  0.5 (49879) |\n",
      "+----------------+--------------+\n",
      "|    M           |  0.5 (50121) |\n",
      "+----------------+--------------+\n",
      "|race            |              |\n",
      "+----------------+--------------+\n",
      "|    B           | 0.33 (33326) |\n",
      "+----------------+--------------+\n",
      "|    O           | 0.17 (16859) |\n",
      "+----------------+--------------+\n",
      "|    W           | 0.50 (49815) |\n",
      "+----------------+--------------+\n",
      "|diabetes        |              |\n",
      "+----------------+--------------+\n",
      "|    N           | 0.67 (66641) |\n",
      "+----------------+--------------+\n",
      "|    Y           | 0.33 (33359) |\n",
      "+----------------+--------------+\n",
      "|disease_severity|0.58/1.39/2.78|\n",
      "+----------------+--------------+\n"
     ]
    }
   ],
   "source": [
    "table1 <- summaryM(age + sex + race + diabetes + disease_severity ~ 1, data = data)\n",
    "print(table1, exclude1 = FALSE, long = TRUE, digits = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## AGE VARIABLE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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09QUJDupXUwHIodAACorMWLF5dodVoz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Pnujo6Krun7h48aJGwgJAXWKwA2BoFOdb\nR4wYsXz5ctV6QkJCp06ddu3atXTp0smTJ+/Zs+fjjz/u379/xReCHTx48PTp0xqMDAB1g2vs\nABgaxf2wQ4YMKVfv0KFDs2bN7t69m5iYGBgYOHr06JycHD8/v8OHD8tkMsVnysrKvv7668jI\nSFtbW03nBoAXxhE7AAYlLS0tMTHxlVde8fX1LdcSiUQDBw787LPPdu7c2aFDh6+//vr58+db\nt27t27evlZWVj4+PXC6/fv16fn7+u+++279/f8X9FqqqetyJIAgLFizw8fFRyy8JAGqMwQ6A\nQVHcNjFkyBDl/bCqBg0a9Nlnn+3evXvFihWmpqbff/99ZGTkN998c/bs2YsXLzo4OAQGBk6c\nOLF3794V75kVqn7ciSAIEyZMqNtfCAD8AyK5XK7tDAAAAKgDXGMHAABgIBjsAAAADASDHQAA\ngIFgsAMAADAQ/wcxULiuiiU4uAAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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g4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAgEMIOACAQwg4A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\nxqlVWVm57VM+/PDDyBFOrSRxu+yyyw4//PAnn3zy9ddfHzx4cLN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      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mypar2()\n",
    "par(mar = c(2,2,2,1))\n",
    "\n",
    "# PLOT AGE DISTRIBUTION\n",
    "plot(\n",
    "    ecdf(data$age), \n",
    "    main = \"\", \n",
    "    xlab = \"AGE\"\n",
    ")\n",
    "\n",
    "age_quantiles <- quantile(data$age, 1:3/4)\n",
    "\n",
    "abline(\n",
    "    v = age_quantiles, \n",
    "    lwd = 3, \n",
    "    col = \"red\"\n",
    ")\n",
    "\n",
    "axis(\n",
    "    3, \n",
    "    at = age_quantiles, \n",
    "    labels = \"Q\" %|% 1:3\n",
    ")\n",
    "\n",
    "hist(\n",
    "    data$age, \n",
    "    freq = FALSE, \n",
    "    xlab = \"AGE\", \n",
    "    main = \"\",\n",
    "    col  = \"lightblue\"\n",
    ")\n",
    "box()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## DISEASE SEVERITY SCORE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TffjEZZtmhR4X29agt//etfoybX2tra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\nAQAAAAgEEjsAAAAAgUBiBwAAACAQ/wM3tUu9UKOfDQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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DVx8kTt2rXvuOOOZs2a1cBaAAAZK/YjdilDhw6tmYUAADKWjzsBAAhEOsNu8uTJ\nbdu2rbpl8+bN77333tf+15FHHvnMM8+kazwAgK+WGnopdpeaN2/esWPHqlvq1KmTSCTGjBmT\nuplIJDp16pSO0QAAvnrSGXaDBw8ePHhw1S25ubm5ublDhgxJ10gAAF9dNRR2y5Ytmzt37vr1\n64uLi/Py8lq0aNG7d28fawcAsB/FHnalpaX9+vWbPXt2fn5+y5YtGzRoUFJSsm7duhEjRvTp\n02fGjBn16tWLewYAgEwQ+8kTV1111Zo1awoLC4uKihYvXjx//vzFixdv2LBh0aJFRUVFw4cP\nj3sAAIAMEfsRuzlz5kybNq179+5VNyYSic6dO0+dOrVv375xDwAAkCFiP2LXoEGD4uLiXd5V\nXFzcsGHDuAcAAMgQsR+xGzhw4JAhQ1avXt23b9+CgoL69euXlpauXbt29uzZEydOHDlyZNwD\nAABkiNjDbsKECbm5uVOmTKn8dLqUgoKCsWPHjh49Ou4BAAAyROxhl0gkxo0bN2rUqCVLlqxb\nt27jxo35+fnNmzfv0KFDdnZ23KsDAGSOGvocu5ycnE6dOrmMBABAfNJ5rVgAAPYjYQcAEAhh\nBwAQCGEHABAIYQcAEAhhBwAQCGEHABAIYQcAEAhhBwAQCGEHABAIYQcAEIgaulYsXyHbt21b\nv7lo7ty5cS90/PHH5+fnx70KAGQOYcfOVrz1xtp/r/zWRf1iXeWTrVt/8uNxN954Y6yrAEBG\nEXbsLJlMdv9m3x/+6t5YV5n4vUvKy8tjXQIAMo332AEABELYAQAEQtgBAARC2AEABELYAQAE\nQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEA\nBELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgB\nAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELY\nAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC\n2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAAQiJ90DkKH+s/7D\nRx999J133ol1lUQiMX78+I4dO8a6CgAcIIQd6bH5P8V1Wx+xo1HTWFeZ/cjvz3iurzcAABaX\nSURBVDrrLGEHQIYQdqRNx+6nXnrdmFiXePGpv8e6fwA4oHiPHQBAIIQdAEAghB0AQCCEHQBA\nIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0A\nQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQd\nAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAgctI9AMTo00+2Pvnkk0VFRbGuUqtW\nraFDh9atWzfWVQDgCwk7Qlb60aZ/vPjSoiXvxLrKirfe7NKlS48ePWJdBQC+kLAjcN++5kdn\nXHRJfPtPJpP92hckk8n4lgCAPeQ9dgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAA\ngRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYAAIEQdgAAgRB2AACBEHYA\nAIEQdgAAgchJ9wAQgv/+7/9+8sknY12iUaNGo0ePzsryjzEAqiXsYJ8kKyqiKHr5zbf+9e/V\n8a3y6SefLFu04Dvf+U7Lli3jWwWArzphB/vBoDE3dDixe3z7//C9VcPPOiWZTMa3BAAB8LIO\nAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCCEHQBAIIQdAEAghB0AQCBc\nKxa+Aj7e/FEURcccc0xWVrz/GGvVqtXrr78e6xIAxEfYwVfAJx+XRlF0yY9+XK9ho/hW+feS\ntx5/+L/j2z8AcRN28JXRpeeZ+c2ax7f/OnXrCTuArzTvsQMACISwAwAIhLADAAiEsAMACISw\nAwAIhLNigf+VTCaTyYULF8a9TsuWLVu0aBH3KgAZSNgB/+O9d5Z++umnXbp0iXuh448/vgby\nESADCTvgf+wo214rN/e+F96IdZVnZv5x4eOPxroEQMYSdkAViUS9Bg1jXSG39kGx7h8gk9VQ\n2C1btmzu3Lnr168vLi7Oy8tr0aJF796927VrVzOrAwBkgtjDrrS0tF+/frNnz87Pz2/ZsmWD\nBg1KSkrWrVs3YsSIPn36zJgxo169enHPAACQCWIPu6uuumrNmjWFhYVdu3bNyvqfT1dJJpNv\nvPHG97///eHDhz/00ENxzwAcOLaUbC4uLr711lvjXuikk07q0aNH3KsAHFBiD7s5c+ZMmzat\ne/fuVTcmEonOnTtPnTq1b9++cQ8AHFDee2fpRyWlf/zr47GusnbVypNffFHYAZkm9rBr0KBB\ncXHxLu8qLi5u2DDet2kDB55k04LDbnjgkVjXeOjWG6P/fBjrEgAHoNjDbuDAgUOGDFm9enXf\nvn0LCgrq169fWlq6du3a2bNnT5w4ceTIkXEPAGSgzf8pXvv222PHjo17oW9/+9vHH3983KsA\n7KHYw27ChAm5ublTpkwZM2ZM1e0FBQVjx44dPXp03AMAGWjNineLN2568p8vxrrKv5e+XVJS\nMmnSpFhXSSQSjRo1inUJIBixh10ikRg3btyoUaOWLFmybt26jRs35ufnN2/evEOHDtnZ2XGv\nDmSsozufMPaeh2JdYmjPLvfee++9994b6ypRFP3+97+//PLL414FCEANfY5dTk5Op06dOnXq\nVDPLAdSA8h07epx34bmDhsS6yvjLLxw6dOgPfvCDWFdJJpM/+clPDj/88FhXqVev3tlnn51I\nJGJdBTJZOq88MXny5Pvvv3/58uWVWyoqKsrKyiovIpmdnX3MMcfUqlVr39f699K36tSrv+/7\nqc6m/2wor6hY8dab8S0RRdHW0tJtn2yNe5Xtn35a+tFHca9SXl6+qWh93Kskk8kNa9fEukqy\noiKKorX/Xln74IPjW+XD91ZFUfTvZW9vKt4Q3yqbitYn4//PeEvJ5u2fbov9P+NPPtlSWhL3\nKjt2lMW6/5TyHWXtTjzpiGPi/YfxY7+9e9SoUbEuUWMOPvjgESNGxLpESUnJmjVrOnToEOsq\nH3/8cb169U444YRYV9m8eXOdOnWaNWsW6yolJSVNmzatU6dOrKts2LDhkEMOiftfDrVr1+7Y\nsWOsS+yTZPo88MADF1xwQdUtTZo02Wm8GTNm7OMqK1eu9JovALBfZGdnf/DBB/sYJzsZNGjQ\noEGD9suuEslkMt3/E/1/3/3ud8vKyu6+++7Uzf31luGPP/64rCz2f1iXlZXtl4OLaV+loqIi\nmUzGXcM7duzIzs6O+99VwfxSrLK3kslkeXl5Tk68L0r4z9gqsS5RM/8Zl5eXJxKJyisIxCSY\nX0oURbVq1drvF80aPHhwFEUPPvjgvu/qwLpWbFZWVu3atfPy8vbv6q5aBgBkAteKBQAIRLyH\nXqMq14otKipavHjx/PnzFy9evGHDhkWLFhUVFQ0fPjzuAQAAMoRrxQIABCL2I3auFQsAUDNc\nKxYAIBCuFQsAEAjXigUACIRrxQIABCL2kycAAKgZwg4AIBDCDgAgEMIOACAQwg4AIBDCDgAg\nEMIOACAQwg4AIBDCDgAgEMIOACAQwg4AIBDhh92OHTtmzpyZ7ilIjzlz5hQXF6d7CtLg3Xff\nXbhwYbqnIA22bdv25z//Od1TkB5PPPFESUlJuqdIs/DDbunSpf3799+0aVO6ByENhg0b9ve/\n/z3dU5AGv/nNb2666aZ0T0EaLFiw4MILL6yoqEj3IKTBwIEDn3vuuXRPkWbhh13qzzuZTKZ7\nENIgmUx6fs9MyWTSX31mqqio8KvPWJ7zo0wIOwCADCHsAAACkTigDlkPHjz4xRdf7Nmz537c\n54YNG/785z8fddRR2dnZ+3G3fCWsWLGicePGjRo1Svcg1LT169dv3779sMMOS/cg1LStW7e+\n99577dq1SyQS6Z6FmvbOO++ccsop7dq1S/cge+35558/+eSTH3zwwX3fVc6+72I/6tevX25u\n7v7dZ/369Zs0aZKV5dhkJsrLyzv44IPTPQVpUK9evfLy8nRPQRrUrl27SZMmqi4zNW7cOD8/\nP91TfBk9e/Y8//zz98uuDqwjdgAAfGmOYwEABELYAQAEQtgBAARC2AEABELYAQAEQtgBAAQi\n5LBLJpM33XTTUUcd1axZs4EDB5aWlqZ7ImpOWVnZx5/lAoLBSyaT7du3X7BgQdUtngQywed/\n9Z4BMsHmzZuvueaaVq1a1a9fv2fPnoWFhantGf6HH3LY3XrrrbfeeusNN9zw+9//fuHChf37\n90/3RNSce++9t/5nrVy5Mt1DEaPt27f/8pe/XLp0adWNngQywS5/9Z4BMsE111zzt7/97e67\n73722WfbtGnTq1evd955J/KHnwxUWVlZy5Ytb7nlltTNVMgvW7YsvVNRY4YNG9arV69/VrF1\n69Z0D0Vcpk6dWrt27dRz2quvvpra6EkgE+zyV5/0DJABSkpKoiiaPn166uaOHTvatm07btw4\nf/gH1iXF9qMlS5asXbu2b9++qZtdu3bNz8+fM2fOUUcdld7BqBnLli3r0aPHqaeemu5BqAkX\nXnjhKaecsm7dujPPPLNyoyeBTLDLX33kGSADrF279oQTTjjttNNSN7Ozs/Py8tauXesPP9iX\nYtetWxdF0aGHHpq6mZWV1bJly/Xr16d1KGrO0qVLX3nlla997Wt5eXlnnHHGSy+9lO6JiNEh\nhxzSsWPHna787UkgE+zyVx95BsgARx999IIFC1q2bJm6+dJLLy1YsOC0007zhx9s2G3cuDGK\novr161duadCgQXFxcfomouaUlpauXbt269at99xzz6OPPtqwYcPTTz/93XffTfdc1ChPAhnL\nM0BGqaioePDBB3v16nXGGWcMHDjQH36wL8Xm5+dHUVRaWpqXl5faUlJSUvk1YTvooINWrVpV\nUFBQq1atKIpOOeWUI4888sEHH7z55pvTPRo1x5NAxvIMkDneeeed7373u6+99tqoUaPGjx+f\nm5vrDz/YI3bNmzePomjt2rWpm8lkct26dS1atEjrUNSQWrVqtW7dOvWcHkVRbm5up06d3n//\n/fRORQ3zJJCxPANkiMLCwq9//et16tRZunTpf/3Xf6VOo/GHH2zYtW/fvmXLlnPmzEndfOON\nN4qLi3v37p3eqagZTz/9dPv27desWZO6uWPHjqVLl7Zv3z69U1HDPAlkLM8AmaCsrKx///79\n+vWbPXt2mzZtKrf7ww/2pdicnJwRI0ZMnDjxmGOOadKkyZAhQ/r06fP5N9gSpFNPPXXLli0D\nBgwYOXJkkyZN7rnnns2bNw8ZMiTdc1GjPAlkLM8AmeDZZ5/94IMPTjrppKeeeqpyY6tWrY49\n9tgM/8MPNuyiKBozZsz27duHDRtWWlp69tln33333emeiBpSt27d2bNnjxw5ctCgQTk5OSef\nfPL8+fMPOeSQdM9FTfMkkJk8A2SC1GcRDxs2rOrGoUOHTp06NcP/8BPJZDLdMwAAsB8E+x47\nAIBMI+wAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7CATvfTSS4nPysnJOfzw\nw7///e+vWLFipwcnEom2bdvutHHBggX9+/dv165dnTp1Wrdu3bt37z/96U8VFRVVH5CoXupC\n3Tv57ne/m7p39erVuxw7jkX3+/5feOGFRCJx2mmn7XKJf/7zn4lEolevXns+7fLlyz9/b3Z2\n9hFHHNGvX7+33nqr6v6r/rKGDx++m/2nHnnHHXckEokOHTqUlZV9ftonn3wykUgcfvjhW7Zs\n2f3/dMABIuRLigG7d9hhh3Xt2jX19YYNGxYtWnTffff94Q9/eOyxx84+++zdfOOvf/3rH/3o\nR1lZWaeddlrXrl03bNhQWFj4zDPPPPTQQ0888UR2dnblIwsKCrp37/75PTRq1GinLZ988slj\njz2W+nrGjBkjR46sgUXj2P/JJ5/cqlWrF1544YMPPigoKNjpMY8++mgURRdffPHeTtu0adOq\nsbhly5a33npr1qxZf/nLX1599dXOnTt/fg+dO3e+6KKLKm8+++yzmzZtOvfcc2vXrp3a0rx5\n86uvvvqhhx5atGjRXXfd9cMf/rDqt5eVlf3oRz+KomjKlCl169b9/P6BA1ESyDyFhYVRFF12\n2WVVN5aXl0+ePDmRSDRo0GDjxo2V26Mo+trXvlZ5c/HixdnZ2S1atHj77bcrN27atOn//J//\nE0XRL3/5y9SWV199NYqiiy++eA9HmjlzZhRFqaA88cQTd7o3pkVj2v/o0aOjKLr99tt32l5R\nUXH44YdnZ2dv2LBhz/f27rvvRlF01lln7bR9x44d11133U537fTLqqpbt25RFBUVFe20/eWX\nX0790tetW1d1+x133BFFUZ8+fSoqKnY/IXDg8FIs8D+ysrLGjh37s5/9rKSk5Pbbb6/uYc88\n80x5efn48ePbt29fubFRo0YPPPBAIpF46qmnvtzqf/rTn6IomjBhQseOHV999dWVK1fWwKIx\n7f/SSy+NouiRRx7ZafuiRYvee++9Xr167ZcL0mdnZ994441RFL322mv7sp+uXbsOGzaspKTk\nxz/+ceXGjRs33nDDDbm5uanXavd1VqCmCDvgM6655pqDDz74zjvvTCaTu3zA+++/H0VRXl7e\nTtvz8vLuvPPOCy+88EssWlJS8vjjj7du3bp79+6pPexURXEsGt/+jz322Pbt2xcWFqZ2Wyn1\nOuy3v/3tfRv2/6tfv36dOnVKSkqq+2XtoUmTJjVr1uyBBx545ZVXUltuvPHGTZs2jRkz5vNv\nrwQOZMIO+IzGjRt37dp106ZNxcXFu3xA6u1cEyZMePLJJ6ueWBBF0TXXXDNs2LAvsehf/vKX\nbdu2XXLJJYlEIvW2sOnTp8e9aHz7TyQSqYN2qdeXKz322GM5OTmpl3f3ixUrVnzyySedO3fe\nx4NqjRo1uu2226IoGjFiREVFxdKlS++5557DDz987Nix+2lSoIY4eQLY2WGHHRZF0cqVK3f5\niuGAAQOmTZv29NNP9+3bt23btuecc06vXr169OjRsGHDzz/4hRde6Nev3+e3n3nmmUOHDq28\nmXoddsCAAVEUderUqW3btm+++eaSJUsqXxiNY9FYf6gBAwaMHz9+xowZqfMPoihatmzZ22+/\n3adPn8aNG+/jtFEUbd269V//+te1116bnZ190003VfewPTdgwIAHHnjgmWee+d3vfjdz5swd\nO3bccccdBx988L7vGahR6X6TH5AGuzx5olLqjNTHHnssdTP63Pvxd+zYMXPmzH79+lU2SnZ2\nds+ePWfNmlX5mNSZAdUZOnRo5SOLiopycnI6dOhQ+Sb91MkHN9xwQ3yLft5+33/qjONVq1al\nbk6ePDmKogcffHBv95Y6eWKX6tat+9xzz1VdNNr7kycqLVu2LDc3t169elEUnXPOOc6ZgK8i\nYQeZaPdhN3DgwCiKXnnlldTN3bRCeXn566+//utf//rYY49NpcaYMWNSd+35Car33ntvFEU3\n3XRT5ZaXX345iqJ27drtsi32y6K7sb/2nzoB5ec//3nq5oknnlirVq1NmzZVPmCvzopt2rTp\nRVWcf/75qXe/devWLfUeu5R9CbtkMjlhwoQoimrXrr1ixYo9+RmBA42wg0y0+7Dr2bNn1QKo\n2goVFRWlpaVbt27d6VsqKiqefvrpvLy8RCKR+sSQPW+gb3zjG9UdkXr99ddjWnSn/cSx/7Vr\n12ZlZXXp0iWZTKbOojj33HOrPmAfP+6kvLx8yJAh0Wc/V2Ufwy51MvIZZ5yx+5GAA5aTJ4DP\n2Lhx46uvvtq4ceOd3gqWkkwmW7Zs+fkP1E0kEt/85jeHDRuW/KJXGHfywQcfzJs375BDDhn6\nWaklUufG7vdF4/6hUlq0aHH66acvWLBg5cqVf/7zn6P9ej5sFEVZWVnXXHNNtM8fd1JV6iQM\nn28CX11OngA+46677tqyZcuoUaN2+f/uWVlZxx133EsvvfTuu+8eeeSRO927cePGKIo+f7mF\n3XjkkUeSyeSgQYN+/vOfV93+yiuvdOvW7ZFHHpk0adJ+X3Qn8e3/0ksvfeaZZ2bMmPH000/n\n5uZecMEFX3rIXWrWrFnlhACRjzsBKlVUVPz85z//2c9+1rBhw2uvvba6hw0aNGjHjh3f+ta3\nKj/zLPW9jz766AMPPNCkSZPKy5TtidT5sKkPB6nqxBNPbN269cqVKxcsWLDfF437h6p04YUX\n5ubm3n///fPmzevTp0+DBg32ZcjqbNiwIY7dAl9FjthB5po3b17lB21s2LDh9ddfLy0tPeig\ng6ZPn76by6p+73vfKywsvP/++7t169amTZs2bdrs2LFjxYoVH3zwQZ06dWbOnFm/fv3KB1f3\nWR5RFE2YMOHggw9esGBBu3btjjvuuJ3uTSQSF1988a233jp9+vQTTzxxPy5aeUpETD9U1f03\natSob9++qddhq14ftqovMW2l1KexvPfee9u3b8/Nzd3NI4FMkcb39wHpkjp5oqrs7OzDDjvs\niiuuWL58+U4Pjnb1fvznnnvuggsuOProow866KBmzZp169ZtzJgxVS82+oVvSpszZ07qA9gm\nTpy4yyEXLVoURdGhhx5aXl6+Hxfdzf8scex/xowZURQddNBBVc9d3au9VXfyREqHDh2iKLr5\n5ptTN3f5y0rZk5MnVq1aFUVRr169dvMY4ECWSO7bhWgAADhAeI8dAEAghB0AQCCEHQBAIIQd\nAEAg/h9aHsiZAXCvLgAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mypar2()\n",
    "par(mar = c(2,2,2,1))\n",
    "\n",
    "# PLOT AGE DISTRIBUTION\n",
    "plot(\n",
    "    ecdf(data$disease_severity), \n",
    "    main = \"\", \n",
    "    xlab = \"DISEASE SEVERITY SCORE\",\n",
    "    xlim = range(data$disease_severity)\n",
    ")\n",
    "\n",
    "disease_severity_quantiles <- quantile(data$disease_severity, 1:3/4)\n",
    "\n",
    "abline(\n",
    "    v = disease_severity_quantiles, \n",
    "    lwd = 3, \n",
    "    col = \"red\"\n",
    ")\n",
    "\n",
    "axis(\n",
    "    3, \n",
    "    at = disease_severity_quantiles, \n",
    "    labels = \"Q\" %|% 1:3\n",
    ")\n",
    "\n",
    "hist(\n",
    "    data$disease_severity, \n",
    "    freq = FALSE, \n",
    "    xlab = \"DISEASE SEVERITY\", \n",
    "    main = \"\",\n",
    "    col  = \"lightblue\"\n",
    ")\n",
    "box()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ASSIGN TREATMENT\n",
    "\n",
    "Treatment will be assigned as a function of disease severity.  Patients with higher disease scores will be more likely to receive treatment 1 (instead of treatment 0).\n",
    "\n",
    "The following plot indicates the probability of assignment by disease severity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ST27JAshAQooDukHi4HiAdCAhTQExJ7dkgYQgIU0BxSzxYDxAUhAQpoCYk9OyQN\nIQEK6A2pR0sB4oOQAAV0hMSeHRKHkAAFtIbUk4UAcUJIgAIaQmLPDslDSIACOkPqwTKAeCEk\nQAFCAhSIPiTeIiGBNIZU/iKAuCEkQAFCAhSIPCTeIiGJ9IVU9hKA+CEkQAFCAhSIOiTeIiGR\ntIVU7gKAOCIkQAFCAhSIOCTeIiGZdIVU5nggnggJUICQAAUICVAg2pA41oCE0hRSecOBuCIk\nQAFCAhSINCTeIiGp9IRU1mggvggJUICQAAWiDIm3SEgsQgIU0BJSOYOBOCMkQAFCAhSIMCTe\nIiG5dIRUxlgg3ggJUICQAAUICVAgupA41oAECxbS1H256x6FFHwoEHc+Q2rM6f1QY6M9SUiA\nxGdIg+QdM0ICJD5D2vvFc7e///77vZ98/317soyQeIuEJPP7Hulo3fBNltVnV26qJyEFHgnE\nn/+DDU+OWXyQkICiAhy1a/nmOEFIQDFBDn9nHlr+bu4WIQGSqD6Q5VgDEi1oSPXV9uUZY3dk\nHQ3wOHSERAsa0gML7MsKp4ktAR6HkJBoke/aBR0ImMB3SHs3rlq2csOe3AQhARKfIbXOEcNr\nZtSMEPMO2ZOBQ+JYA5LNZ0hXTW7syF5lmmqX2pPlhxR8DQED+AxpZEP+xo5R9iUhARKfIVVv\nyt/YOsm+JCRA4jOk1YPX7Wppa9m9ftgaezJoSLxFQsL5DClTP9rpoGptxp4kJEDi+/B3W3PD\n5obm9txE2SEFXT3ADNF8IEtISDhCAhSIJCTeIiHpog0p4MMApiAkQAFCAhQgJECBKELiWAMS\nL9KQAj4KYAxCAhQgJEABQgIUiCAkjjUg+aIMKeCDAOYgJEABQgIUICRAgfBD4lgDUoCQAAUi\nDCngYwAGISRAAUICFCAkQIHQQ+JYA9IgupACPgRgEkICFCAkQAFCAhQIOySONSAVIgsp4CMA\nRiEkQAFCAhQgJECBkEPiWAPSIaqQAj4AYBZCAhQgJEABQgIUICRAgXBD4qAdUiKikAIuHzAM\nIQEKEBKgACEBCoQaEscakBbRhBR0rQDDEBKgACEBChASoECYIXGsAalBSIACkYQUeK0AwxAS\noAAhAQoQEqBAiCFxrAHpEUVIwdcKMAwhAQoQEqAAIQEKEBKgQHghcdAOKRJBSGWsFWAYQgIU\nICRAAUICFCAkQIHQQuKgHdIk/JDKWSvAMIQEKEBIgAKEBCgQVkgca0CqhB5SWWsFGIaQAAUI\nCVCAkAAFCAlQIKSQOGiHdAk7pPLWCjAMIQEKEBKgACEBChASoEA4IXHQDikTckhlrhVgGEIC\nFCAkQAFCAhQgJEABQgIUCCUkOkLaEBKgACEBChASoAAhAQoQEqBAGCFxyipSJ9SQyl4rwDCE\nBCjgN6S2f3ux3drxP25/1ZkiJEDiM6TXzxXi9OZhZ44e/Lw9SUiAxGdIC6Y+9/qyft/LtC+e\na08SEiDxGVLFv1rWAbHDsp45xZ70DImDdkgfnyGN3GZZmSves6ynh9qT/kJStIpA/PkM6Vtf\neOpj+/oPC79iXxESIPEZ0n/OFhdnr148eXj3BxsICenj9/B35s2XspdvPviBM0VIgCSED2QJ\nCekTNKT6avuyctDs2bPnbC8+CyEhfYKG9MAC+3L6GXV1dTe/WnQOOkIKlbdrd801pe8jJKSQ\n75D2bly1bOWGPbkJQgIkPkNqnSOG18yoGSHmHbInCQmQ+AzpqsmNHdmrTFPtUnuSkACJ31OE\nGvI3doyyLwkJkPgMqXpT/sbWSfalR0icsoo08hnS6sHrdrW0texeP2yNPeknJGWrCMSfz5Ay\n9aOdOqrWZuxJQgIkvg9/tzU3bG5obs9NEBIgUf6BLCEhjQgJUICQAAVUh8TRb6RSaCH1aK0A\nwxASoAAhAQoQEqAAIQEKEBKgQFgh9WilANMQEqBASGc29GSVAPOo/xYhIIUICVCAkAAFCAlQ\ngJAABQgJUICQAAUICVCAkAAFCAlQgJAABQgJUICQAAUICVCAkAAFCAlQgJAABQgJUICQAAVC\nCOmtp8tfHV2a9uheg+AeP6B7DYJ7+JjuNQjsyCO+ZgshpLUzAi4tBhYt170GwU36O91rEFir\naNK9CoE91SvjZ7YQQqo/P+DSYuCbN+heg+Am3q97DQL7RLyoexUC2yYIyT9CigQhFSCkGCCk\nSIQb0pnfLu3zA88xzskVutcguH6n6V6DwM4UE3SvQmDjhcdr/YQLygrp/3ot8ivm/Qc+Z8w4\n3WsQXMr+1AsAAAZkSURBVOUZutcguFPO1L0GgZ15qq+Qvv235YQEoAhCAhQgJEABQgIUICRA\nAUICFCAkQAGFIWVumzTq6lZ1y4vCsUO2Dt2rEUDm7Bcs057r3Dob9Fx/fMPYwRc/G+hpVhjS\n7Sc99Ptz5qpbXhTudv5c5z7dq+Hf0R8L+0Vp1HOdX2eDnuvFYx99/pqBrwR5mtWF1DZ6rWU1\nileULTAKy2Y9nXVE92r4dl9/Yb8ojXqu8+ts0HPdKjZbVvvEFUGeZnUhNYtmy+oYvlHZAqNw\nyWrdaxDMB7set1+URj3X+XU26Lnee9672csvLQ3yNKsLqUG0ZC9rVilbYBRGf+2MYV9p1L0W\nQbxtvygNe66ddTbtuW7s9fMgT7O6kDaLtuzljGXKFhiBVjFz6z9fPuDfda9HAM6L0rDn2lln\ns57rjgcGzToa5GlWvkVaqWyBETj2xrHse+FxK3SvRwDuLZIpz7WzzkY9169M7/eXnwV6mlW+\nR9ptWZkRG5QtMDKXLda9BgG8nXuPZNRzndu1c5jxXD876CuvW8GeZpVH7e60rCZh1JfybD37\n7eyKV/9I93oE8HbuqJ1Rz7WzzgY918eqltj7dIGeZpWfI1U0/L/aeeqWF4FPx375kaf/eMQH\nutcjgNz/3c16rp11Nui53iru/cesnUGeZpVnNvxV9aglh9QtLwp7vjb0lK+b8XFMXi4ks57r\n3Dqb81zf43x0LK4P8jRzrh2gACEBChASoAAhAQoQEqAAIQEKEBKgACEBChASoAAhhanR+YS8\nz7jrXnUmRbVz9cKVZw0YP2uT/e0FL4jjKnMjlgjxVn6w12we9z8tvpyf4SlxiTxyX+5W7wkL\ndx9fneWd94vqu8U5+T+r9zsx7tMwn5cEIqQwNYqxCxcuvHCwGPCYPZkLab3offGfzD1ZzGm3\nC6hamHOtM+DIECHuyI31ms3r/o5x4p3cHN8VP5VH7hOj7FuXjhV9m/Krc7/9gwoxP3u5vO0L\nYr0z8NjZwt9ffUQnQgpTo3B+a6Dj9l4n27/Z4oS0q89pL2evDl5uF/OCWCQNeFhcKr7k3PKc\nzfP+H4q7nOvM+D4fyPfsE7kv8mj/rnMjv4G0rGki90dpt/c6eb99fY+Y5+svA+EEQgpTPiTL\n+itxi5V/5d4lnD8DYrX0mt21kIXi2RrxmtXdbJ73vyRyf+/tRTHHKh6S9YkYaRUJybpB/Fn2\n8qOKfkZ810+sEFKYOkP6cFBFJv/KvUn8KvezjX/bpZBPBpyeuUXUW93M5n1/5hzxpn39l+Ln\npULKDOyfKRbSwUqx3bL+XJjyZRAxQkhh6gzJmik+yL9yHxSTftf5LYkFhTwobrZ2iilWN7N1\nc/8a8RP7anLfD0uFtE9Ms4qFZP1vMbVjT9/xh4P9M0FI4ToR0p+I5/Kv3La5Qkz8i0c/dn58\n4ljAffbkPLHTykwUL3czm+V9/6tOJnvFvMJ78iEd3j69T4NVNKTMLPGLy8RvwntGEouQwnQi\npO/bx8Fyr9z2h688RYg+M7dY7uPW12enDvSdnLEPFtzqPVuOx/1TxRuWdbv4ReE9+47fPulJ\ne7YiIVmv9BssLuNIQ3CEFCb3Ful51yu346U7pwhRV7hPdq9Yk73cLs7OeM7WqdT9d4kfW9aX\nPnfQ6rJr5xz+/sZEMc3+QutiIVm3iP6vlfvPTTNCCpP7PdKB3Cs3cyj3pb2Z31f0ermggIuP\nbzFe8pzN+bnX/e/1rrXeEvPtm0XfI3V82zlCXjSk18Ul5f97U4yQwtQZ0kcnnZI/TNYxZEr+\nzpXil/Lr/J1eI6+3TRcrvGZzeN8/S7x2j3jQvlX8YMNOscQqEdIbYlY5/9LUI6QwuT5Hsr/4\n2nnlfrlv/stG/7t4Qn6d/0T8wLneLs7IeMyW43n/34nbZ/b7xL5VPKT9zuaKkBQipDAdP7Nh\nXa+h9hsW55X7c/H57fbPtvQb0Sq/zmtFk3OdOT37hqr0bDme9x/sN7H3AudWqZCmWoSkFCGF\nKX+u3RD3uXaZa4WYcMlFVWLgNvfR6YU793UeZKgTN5WeLb9o7/svF2KTc0O6pzOkP4jKo4Sk\nFCGFKX/299hrpbO/n1xw1oDKaXX2aW0njk6Lx9eI2/LDmsSYjpKzdS7c6/6/FwNyf2hOuqcz\nJGuyffoEISlESIAChAQoQEiAAoQEKEBIgAL/HyqrUPv8NrgiAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigmoid <- function(x) 1/(1 + exp(-x))\n",
    "probability_treatment <- sigmoid(log(1+data$disease_severity) - mean(log(1+data$disease_severity)))\n",
    "data$treatment <- rbinom(N, 1, probability_treatment)\n",
    "mypar2()\n",
    "plot(\n",
    "    data$disease_severity, \n",
    "    probability_treatment,\n",
    "    xlab = \"DISEASE SEVERITY\",\n",
    "    ylab = \"PROBABILITY OF TREATMENT\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OUTCOME SCORE\n",
    "\n",
    "The outcome score will be a function of age, disease severity, and treatment.\n",
    "\n",
    "$$\n",
    "E[Y] = 9 + 2 \\cdot \\textrm{log}(\\textrm{age}) + 30 \\cdot \\textrm{sigmoid}(\\textrm{disease_severity}) - 8 \\cdot \\textrm{treatment 1}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mean_response <- 9 + log(data$age) + 16 * sigmoid(4 * (data$disease_severity - mean(data$disease_severity))) - 2 * data$treatment\n",
    "error_term <- rnorm(N, 0, 2)\n",
    "data$outcome <- mean_response + error_term"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NAIVE COMPARISON OF OUTCOME AND TREATMENT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JoaQ7O42KE6gBhCjx0AOOmyyy5777336rOxcI0pxyS5M84wLJtw8+MMEKHHDgAc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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = outcome ~ treatment, data = data)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-15.262  -5.629  -2.508   6.946  19.050 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) 17.20680    0.03132   549.4   <2e-16 ***\n",
       "treatment    1.41795    0.04431    32.0   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 7.006 on 99998 degrees of freedom\n",
       "Multiple R-squared:  0.01014,\tAdjusted R-squared:  0.01013 \n",
       "F-statistic:  1024 on 1 and 99998 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LJj2gAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mypar2()\n",
    "plot_ecdf <- function(x){\n",
    "    plot(\n",
    "        ecdf(x$outcome), \n",
    "        add = TRUE, \n",
    "        col = x$treatment + 1, \n",
    "        lwd = 3\n",
    "    )\n",
    "    points(median(x$outcome), .5, col = \"white\", pch = 16, cex = 4)\n",
    "    points(median(x$outcome), .5, col = x$treatment + 1, pch = 1, cex = 4)\n",
    "    text(median(x$outcome), .5, x$treatment, cex = 2, col = x$treatment + 1)\n",
    "}\n",
    "\n",
    "plot.new()\n",
    "plot.window(xlim = range(data$outcome), ylim = c(0,1))\n",
    "garbage <- by(data, data$treatment, plot_ecdf)\n",
    "box()\n",
    "axis(1)\n",
    "axis(2)\n",
    "\n",
    "lm1 <- lm(outcome ~ treatment, data = data)\n",
    "summary(lm1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## COMPARISON OF TREATMENT GROUPS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Descriptive Statistics  (N=100000)\n",
      "\n",
      "+----------------+--------------+--------------+\n",
      "|                |0             |1             |\n",
      "|                |(N=50044)     |(N=49956)     |\n",
      "+----------------+--------------+--------------+\n",
      "|age             |   43/54/60   |   43/54/60   |\n",
      "+----------------+--------------+--------------+\n",
      "|sex             |              |              |\n",
      "+----------------+--------------+--------------+\n",
      "|    F           |  0.5 (24850) |  0.5 (25029) |\n",
      "+----------------+--------------+--------------+\n",
      "|    M           |  0.5 (25194) |  0.5 (24927) |\n",
      "+----------------+--------------+--------------+\n",
      "|race            |              |              |\n",
      "+----------------+--------------+--------------+\n",
      "|    B           | 0.33 (16706) | 0.33 (16620) |\n",
      "+----------------+--------------+--------------+\n",
      "|    O           | 0.17 ( 8431) | 0.17 ( 8428) |\n",
      "+----------------+--------------+--------------+\n",
      "|    W           | 0.50 (24907) | 0.50 (24908) |\n",
      "+----------------+--------------+--------------+\n",
      "|diabetes        |              |              |\n",
      "+----------------+--------------+--------------+\n",
      "|    N           | 0.67 (33368) | 0.67 (33273) |\n",
      "+----------------+--------------+--------------+\n",
      "|    Y           | 0.33 (16676) | 0.33 (16683) |\n",
      "+----------------+--------------+--------------+\n",
      "|disease_severity|0.41/1.00/2.05|0.88/1.89/3.48|\n",
      "+----------------+--------------+--------------+\n",
      "|outcome         |   13/15/22   |   12/17/26   |\n",
      "+----------------+--------------+--------------+\n"
     ]
    }
   ],
   "source": [
    "table2 <- summaryM(age + sex + race + diabetes + disease_severity + outcome ~ treatment, data = data)\n",
    "print(table2, exclude1 = FALSE, long = TRUE, digits = 2)"
   ]
  }
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